CS201 Data Structures Lecture 11

Deleting a node with no children in a Binary Search Tree (BST) is simple. Just remove the node without needing to rearrange any pointers.

Deleting a node with one child in a Binary Search Tree (BST) involves replacing the deleted node with its single child. The parent of the deleted node is now connected to the child.

Deleting a node with two children in a Binary Search Tree (BST) is the most complex case. You need to replace the node with either the largest node in its left subtree (InOrder Predecessor) or the smallest node in its right subtree (InOrder Successor).

A Binary Search Tree (BST) is a data structure where each node has a value, and the values in the left subtree are smaller, while values in the right subtree are larger.

The process of adding new nodes to a Binary Search Tree (BST) while maintaining the BST property of ordered nodes. The new node is placed in the correct position based on its value.

A popular way to traverse a Binary Search Tree (BST) that involves visiting the root node, then the left subtree, and then the right subtree. The output is the root node followed by its left subtree and then its right subtree.

A common method for traversing a Binary Search Tree (BST). It involves visiting the left subtree first, then the root node, and finally the right subtree. This results in an outputs nodes in ascending order.

A traversal method for visiting nodes in a Binary Search Tree (BST). It involves visiting the left subtree, followed by the right subtree, and lastly the root node. The output is the left subtree nodes, followed by the right subtree nodes, and finally the root node.

The process of finding a specific node in a Binary Search Tree (BST) based on its value. The search starts at the root node and follows a path based on the value comparison until the target node is found.

The smallest node in a Binary Search Tree (BST) is found by moving to the leftmost child recursively until reaching a node with no left child.

The largest node in a Binary Search Tree (BST) is found by moving to the rightmost child recursively until reaching a node with no right child.

Binary Search Trees (BSTs) have a potential drawback of becoming unbalanced, leading to inefficient search times. This happens when insertions are done in a specific sequence that creates a long, skewed path.

An AVL tree is a self-balancing Binary Search Tree (BST) that ensures a balanced structure by maintaining a specific balance factor for each node. The balance factor is the difference in height between the left and right subtrees.

The difference in height between the left subtree and the right subtree of a node in an AVL tree determines the balance factor. A balance factor of 0, +1, or -1 maintains balance.

A node in an AVL tree is considered balanced if its balance factor is -1, 0, or +1. This ensures that the tree maintains an optimal shape for efficient search operations.

The height of a subtree is the number of edges along the longest path from the root of the subtree to its farthest leaf node.

An AVL tree is a self-balancing Binary Search Tree (BST) that ensures efficient search operations by maintaining a balanced structure. It's a popular choice for data structures that require fast lookups and insertions.

AVL trees maintain balance during insertions and deletions by performing rotations. These rotations are specific operations that rearrange nodes to ensure the balance factor remains within acceptable limits.

A specific operation that helps to balance an AVL tree. It involves rearranging the nodes to adjust the balance factor.

A more complex rotation used in AVL trees to balance the structure when a single rotation is not sufficient. This operation involves a combination of single rotations.

A type of rotation used in AVL trees to restore balance during insertions or deletions. It's a specific sequence of single rotations used to address a particular balance factor violation.

Inorder traversal of a Binary Search Tree (BST) produces a sorted sequence of values. This is because it visits the left subtree first in ascending order, then the root, and finally the right subtree.

A type of rotation used in AVL trees to restore balance during insertions or deletions. It's a specific sequence of single rotations used to address a particular balance factor violation.

Inorder traversal of a Binary Search Tree (BST) produces a sorted sequence of values. This is because it visits the left subtree first in ascending order, then the root, and finally the right subtree.

The process of deleting a node from an AVL tree while maintaining the tree's balance. This involves identifying the correct replacement node, making the deletion, and then performing rotations if necessary to rebalance the tree.